The following is a brief summary of some of thoughts said over by R' Frand on the parsha this evening. I have attempted to reproduce these vorts to the best of my ability. Any perceived inconsistency is the result of my efforts to transcribe the shiur and should not be attributed to R' Frand.
R' Frand began the vort by quoting the famous Ba'al HaTurim which observes that from the time of Moshe's birth until Sefer Devarim, Moshe appears in every parsha in the Torah except for Tezaveh. R' Frand offered three unique explanations for why.
The first explanation was said in the name of the Ba'al HaTurim himself, albeit with an interesting twist. The Ba'al HaTurim explains that this results from Moshe having said in Parshas KiSissa (Shemos 32:32) that he should be wiped out of the Torah if Hashem were to destroy the Jews. Although Moshe's conditional request did not come to fruition, the words of a Tzaddik have power and he was omitted from this parsha.
But why was it specifically Parshas Tezaveh? R' Frand quoted the Sefer Ateres Dudaim which quotes R' Moshe Einstader who linked this to Moshe's initial conversation with Hashem about leading the Jews out of Egypt. Over the course of seven days, Moshe and Hashem had a discourse where Hashem attempted to convince Moshe that he was the man who lead the Jews out of Egypt and Moshe tried to turn the job down. At one point during the conversation Hashem became angry with Moshe and it states at Shemos 4:14 "Vayichar Af" that Hashem became angry and then said --is this your brother Aharon the Levi and Moshe was happy when he saw him.
R' Frand quoted Rashi which cites a Gemara in Zevachim which states that every time the words "Vayichar Af" are used, there is a punishment. R' Yehoshua Ben Carcha says there that this is the one time that there was no punishment, but R' Yosi disagrees and states that Moshe is punished. Since the pasuk calls Aharon "the Levi" it is a sign that Aharon was meant to be a Levi and Moshe would be a Cohen. However, due to Moshe's resistance to taking the role of leader, he lost the Kehuna.
R' Einstader explained that this is why Moshe is not mentioned in Tezaveh. Because this parsha contains extensive discussions of the clothing of the Cohanim and is irrelevant to Moshe because he is not one.
R' Frand also quoted the Klei Yakar who also notes that Parshas Tezaveh is about the clothing of the Kehuna and that since Moshe was so happy for his brother Aharon who received this role, he took himself out of the picture (so to speak). He connects it with the pasuk in Tehillim - Hinei Ma Tov U'Manayim Sheves Achim Gam Yachad - which is emblematic of Moshe's relationship with his brother.
The last explanation came from the Ba'al HaTurim who writes that the reason that Moshe was omitted from Tezaveh was because of Hashem's sensitivity to Moshe's feelings. Since Moshe was no longer destined to be a Kohain, Hashem was sensitive to Moshe and did not address Moshe "laimor" -- to teach others as to things which he could not receive.
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